Beyond Artistry: Da Vinci's infamous 'Rule of Trees' faces new round of scientific scrutiny after 500 years

Leonardo Da Vinci, like us, marvelled at the changing seasons and the falling leaves of chameleon-like trees during autumn. Yet, his genius went beyond admiration; he observed a remarkable pattern in tree growth.

Da Vinci noted that while trees displayed unique appearances, they all shared an intriguing characteristic. When you added up the thickness of branches at the same level, it always equaled the width of the tree's main trunk.

Although Da Vinci's 'Rule of Trees' likely served as artistic guidance, it also piqued the interest of those with a scientific mindset. Researchers developed various models to explain this phenomenon, suggesting it might be related to how trees transport water to their upper reaches, possibly for wind resistance.

Surprisingly, physicists attempting to model trees for optimal branching thickness against wind found themselves rediscovering Da Vinci's now infamous Rule of Trees. This suggests that trees may have evolved this way to withstand strong winds, and only Leonardo managed to document this phenomenon.

After confirming the structural validity of this theory, scientists turned to investigate its implications for tree hydraulics. However, a recent study has revealed a disconnect between Da Vinci's rule and the science behind tree physiology.

While Da Vinci likely never intended his theory as an absolute rule, a group of researchers sought to explore its potential for mapping tree carbon storage and drought vulnerability.

"Many models in biology have drawn from Leonardo's rule to describe both tree branching patterns and vascular systems, even though there's limited evidence of consistent application," the authors explain in their paper.

Trees continually transport water and nutrients to their upper extremities, a process that becomes more challenging with height. Consequently, their vascular systems must be optimised to facilitate this circulation in the tallest branches.

Contrary to Da Vinci's suggestion of gradually thinning the more the trees branch, the researchers' models revealed that vascular channels must actually widen as they ascend to maintain sufficient force for water transport. This adaptation conserves carbon needed for building the tree's water transport network.

"Our goal was to establish a ratio for estimating tree biomass and carbon in forests," says Sopp, an environmental scientist. This ratio will also refine the 'metabolic scaling theory,' which predicts how plant attributes like height, biomass, diameter, and leaf area change with size.

Sopp notes, "This new ratio will aid in calculating global carbon capture by trees." The authors also hope that their models will shed light on why larger trees are more susceptible to drought, a problem exacerbated by climate change.

The findings of this research have been published in PNAS and can be accessed here.